Timeline for $A_{\infty}$ multiplications on Morse cochain complex
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 12, 2020 at 13:57 | comment | added | Pavel | Just a note about the degree condition: If the coefficient of $m_k(x_1,\dotsc, x_k)$ at $x_{k+1}$ is non-zero, then the Morse indices satisfy $\mu(x_1) + \dotsb + \mu(x_k) - \mu(x_{k+1}) + k - 2 = 0$, which is the dimension-$0$-condition on the moduli space of Morse trees. Assuming that the Morse complex of $S^n$ is generated by one generator $S$ in degree $0$ and one generator $N$ in degree $n$, the only solution of this equation for $k\ge 3$ is for $k = n+2$ and $x_1 = \dots = x_k = S$, $x_{k+1}=N$. I would guess that this must be also zero for some geometric reasons. | |
| Apr 10, 2019 at 12:25 | history | edited | Arun | CC BY-SA 4.0 |
added 44 characters in body
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| Apr 4, 2019 at 8:33 | comment | added | Arun | We fix the Morse function and perturb the gradient flow trees, thx. | |
| S Apr 3, 2019 at 7:46 | history | suggested | LeechLattice |
add tags with more generality
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| Apr 3, 2019 at 0:10 | review | Suggested edits | |||
| S Apr 3, 2019 at 7:46 | |||||
| Apr 2, 2019 at 16:16 | comment | added | Daniel Pomerleano | Typically one needs to choose more data (e.g. several Morse functions or some other perturbation data on Stasheff trees) to define these operations? Probably the answer to your question will depend on how you choose this data... | |
| Apr 2, 2019 at 8:44 | history | asked | Arun | CC BY-SA 4.0 |